In the given figure, l is a line intersecting the two concentric circles, whose common center is O, at the points A, B, C, and D. Show that AB = CD.  Let OM be perpendicular from O on line l. We know that the perpendicular from the centre of a circle to as chord; bisect the chord.Since BC is a chord of the smaller circle and OM ⊥ BC.∴ BM = CM ....(i)Again, AD is a chord of the larger circle and OM ⊥ AD.∴ AM = DM ....(ii)Subtracting (i) from (ii), we get,AM - BM = DM - CM ⇒ AB = CD Hence proved. Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof) Is there an error in this question or solution?
Given: A line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D.To Prove: AB = CD.Construction: Draw OM ⊥ BC. ⇒ AB = CD.
SolutionGiven : Two concentric circles with O. A line intersect them at A, B, C, and D To prove: AB=CD construction: Draw OM ⊥ AD, In bigger circle AD is chord OM ⊥ AD. Proof ∴AM=MD [⊥ from centre of circle of a circle bisects the chord] ——–(i) The smaller circle : BC is chord OM ⊥ BC BM=MC [⊥ from centre of the circle of a circle bisects the chord] ————–(ii) On subtracting (i) from (ii) AM-BM=MD-MC AB=CD Hence Proved
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Hence Proved
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Two concentric circles are intersected by a line l at a, b, c and d. then
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